Analytic Combinatorics in Several Variables

This book by Robin Pemantle and Mark C. Wilson is aimed at graduate-level researchers in the field of analytic combinatorics, and more experienced researchers in fields in which enumerative questions arise that can be solved by the methods of analytic combinatorics. In contrast to the magnum opus of Flajolet and Sedgewick, this book deals almost exclusively with problems involving more than one variable.

Robert Sedgewick in Bulletin of the American
Mathematical Society (July 2018): "The organization of the book is exemplary ...
The treatment of analytic methods for multivariate generating functions
in this book is breathtaking ... Whether or not one cares about
applications, this book is an extremely well- written treatment of a
relevant contemporary topic that many mathematicians will see as an
opportunity to learn and appreciate new areas of mathematics and how
they interact."

Bruce Richmond in Mathematical Reviews:
"This book is a timely and well-written description of contemporary
multivariate analytic combinatorics, and the authors deserve much credit
for the progress since 1995. The book is written as a text with helpful
exercises to illuminate the concepts; students will see several branches
of modern mathematics and computer algebra interact. "

Michael Albert
in New Zealand Mathematical Society Newsletter, Dec 2013:
"Since roughly the turn of this century the authors have been at the
forefront of the development of more general, less ad hoc, techniques
for such and related problems. This book develops, summarises and
illustrates the results of their work both theoretically and in
practice. As such, it fills a gap that was very much in need of filling."
... "I for one am very grateful to have it on my desk now."

D.V. Feldman in Choice 51.6 (Feb 2014), 1048: "Few books ever made a better case for the grand unity of mathematics." ...
"It deserves a place on college library shelves even if nearly all
undergraduates will find it too daunting, for it provides a nearly
universal answer to the 'what can I do with this stuff?' question that
students pose in so many basic courses. Recommended."